Ideally, a valid density estimator would also be a good synthesizer and a good defender. However, synthesis quality and density modeling are goals that tend to be at odds with each other. High-quality synthesis is easier to achieve using shortrun sampling with a defective density rather than long-run sampling with a stable density [1]}. Unfortunately, models with high-quality shortrun synthesis lack the stability needed for defense. The EBM defense from [2]} advocates for the use of a valid density approximation to stabilize trajectories, but this requirement might be too strict given the difficulty of density estimation. Learning midrun sampling trajectories sufficient for defense is much more feasible for complex datasets such as ImageNet than full density estimation, even if longrun samples from the defensive model are not realistic. Our work is the first to explore this possibility. The overarching purpose of this paper is to discuss techniques for building sample paths from shortrun to longrun, with the hope that these techniques will eventually enable both high quality synthesis and defense to be accomplished with a model that is also a valid density. For now, the difficulty of valid density modeling leads us to restrict our focus to separate time scales of the sampling regime necessary for each task. Interestingly, EBM training naturally accommodates learning at different trajectory lengths.
